1. **Problem Statement:** A firm must choose between two production systems A and B with given costs, lifespans, operating costs, and other expenses. We need to compute the Equivalent Annual Cost (EAC) for both systems and decide which system to choose. 2. **Formula for EAC:** The Equivalent Annual Cost (EAC) is calculated as: $$EAC = \text{Present Worth} \times \text{Capital Recovery Factor (CRF)}$$ where $$CRF = \frac{i(1+i)^n}{(1+i)^n - 1}$$ Here, $i$ is the discount rate and $n$ is the life of the system. 3. **Calculations for System A:** - Initial cost = 300000 - Life = 4 years - Annual operating cost = 70000 - Major overhaul in Year 3 = 90000 - Discount rate $i = 0.11$ Calculate CRF for $n=4$: $$CRF_A = \frac{0.11(1+0.11)^4}{(1+0.11)^4 - 1} = \frac{0.11 \times 1.5187}{1.5187 - 1} = \frac{0.167}{0.5187} \approx 0.322$$ Calculate present worth (PW) of overhaul at Year 3: $$PW_{overhaul} = \frac{90000}{(1+0.11)^3} = \frac{90000}{1.3676} \approx 65830$$ Calculate PW of annual operating costs (annuity for 4 years): $$PW_{operating} = 70000 \times \frac{1 - (1+0.11)^{-4}}{0.11} = 70000 \times 3.102 = 217140$$ Total PW for System A: $$PW_A = 300000 + 217140 + 65830 = 583970$$ Calculate EAC for System A: $$EAC_A = PW_A \times CRF_A = 583970 \times 0.322 \approx 188679$$ 4. **Calculations for System B:** - Initial cost = 500000 - Life = 7 years - Annual operating cost = 55000 - Salvage value = 80000 - Discount rate $i = 0.11$ Calculate CRF for $n=7$: $$CRF_B = \frac{0.11(1+0.11)^7}{(1+0.11)^7 - 1} = \frac{0.11 \times 2.105}{2.105 - 1} = \frac{0.2315}{1.105} \approx 0.209$$ Calculate PW of salvage value: $$PW_{salvage} = \frac{80000}{(1+0.11)^7} = \frac{80000}{2.105} \approx 38020$$ Calculate PW of annual operating costs (annuity for 7 years): $$PW_{operating} = 55000 \times \frac{1 - (1+0.11)^{-7}}{0.11} = 55000 \times 4.5638 = 251009$$ Total PW for System B: $$PW_B = 500000 + 251009 - 38020 = 712989$$ Calculate EAC for System B: $$EAC_B = PW_B \times CRF_B = 712989 \times 0.209 \approx 148015$$ 5. **Decision:** Since $EAC_B = 148015$ is less than $EAC_A = 188679$, System B should be chosen as it has the lower equivalent annual cost. **Final answers:** - a) $EAC_A \approx 188679$ - b) $EAC_B \approx 148015$ - c) Choose System B